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For N=100, though, they could know beforehand that potential solutions are eliminated at least the first 15 times someone says "I don't know". For any N, it sh
by vintermann 5y ago
For N=100, though, they could know beforehand that potential solutions are eliminated at least the first 15 times someone says "I don't know". For any N, it should be possible to work out the longest such a game could go on (until one of them says, "I don't know, and I don't know any more from your last statement").
- refurb 5y agoI would assume it hinges on the fact that when one party says "I don't know the answer" then they are eliminating a possibility (which isn't intuitive at all with that answer).
- vintermann 5y agoI believe (I could be wrong here, I haven't rigorously checked this) that when the numbers are less than 100 and both parties know this, there will always be a possibility eliminated by a "I don't know" statement.
- caf 4y agoAfter the round in the posed problem, it reaches a stalemate. If Peter had said "I don't know the numbers" at the end there, Sandy can exclude the possibility that the numbers were 77 and 84. However, at this point Peter already knows that Sandy still doesn't know the numbers: Even if the sum Sandy was told was 161, there are still five remaining live possibilities for that sum (62 + 99, 65 + 96, 70 + 91, 76 + 85 and 80 + 81), so Peter gains no new information from Sandy's next statement that Sandy does not know the numbers.